I'm trying to figure out how to play AAxx post flop, especially when you whiff at your set, the flop is trash (no redraws) and you get aggression before you. At what stack/pot ratio do you call anything vs folding to a leadout pot bet or even to a check-raise?

If you only have, say, 25% or less of your stack invested preflop with AAxx and completely airball the flop, you can fold if someone leads out for the pot (unless they're just completely erratic and insane). On this particular hand though, you can get so much of your stack in preflop against the small blind that the flop doesn't matter: you're going to raise all-in if he leads the flop for the pot. Other reasons it's a good play are because: he might just fold preflop and he might just re-pot you preflop.

Look at it this way: if your opponent could see this thread, he'd be so glad you folded instead of re-potting.